[tex]\frac{3}{17}+6[/tex]
Answer (2)
Rewrite the whole number 6 as a fraction with a denominator of 17: 6 = 17 6 × 17 = 17 102 .
Add the two fractions: 17 3 + 17 102 = 17 3 + 102 .
Calculate the sum of the numerators: 3 + 102 = 105 .
Express the result as a simplified fraction: 17 105 .
Explanation
Understanding the problem We are asked to evaluate the expression 17 3 + 6 . This involves adding a fraction to a whole number. To do this, we need to express the whole number as a fraction with the same denominator as the given fraction.
Rewriting the whole number First, we rewrite the number 6 as a fraction with a denominator of 17. To do this, we multiply 6 by 17: 6 = 17 6 × 17 .
Calculating the numerator Now, we calculate 6 × 17 = 102 . So, 6 = 17 102 .
Adding the fractions Next, we add the two fractions: 17 3 + 17 102 = 17 3 + 102 .
Simplifying the fraction Now, we calculate 3 + 102 = 105 . Therefore, 17 3 + 17 102 = 17 105 .
Final Answer The fraction 17 105 is already in its simplest form because 105 and 17 do not share any common factors other than 1. Thus, the final answer is 17 105 .
Examples
Fractions are used in everyday life, such as when baking a cake, measuring ingredients, or splitting a bill with friends. Understanding how to add fractions and whole numbers is essential for accurate calculations in these scenarios. For example, if you need to add 17 3 of a cup of flour to 6 cups of flour, you would perform the calculation we just did to find the total amount of flour needed.
To find 17 3 + 6 , first convert 6 to a fraction with the same denominator, yielding 17 102 . Adding these gives 17 105 , which is in simplest form. Therefore, the final answer is 17 105 .
;
